Sasuke has Karin's Chakra (through Uzumaki blood line, being the descendants of Asura Ōtsutsuki) too, since he had used her ability to heal himself by drinking her blood.
First of all I would like to correct this misconception. Sasuke obtained his rinnegan powers After receiving half of Hagoromo Ōtsutsuki's chakra, not by drinking the blood of karin.
Ninjutsu haven't been shown to have any form of lingering chakra effects, making it highly unlikely this one would have had. The chakra would likely be used up immediately to heal said critical wounds.
Now coming back to your original question
My question is, if Sarada possess Indra's and Asura's Chakra, can she awaken the Rinnegan, as the way Sasuke had did?
Yes, if she has both types of chakra, which is highly likely due to Sasuke having both, she could. But not in the same way as Sasuke did, as this would require Hagoromo Ōtsutsuki's to sacrfice his chakra to her.
However the likelihood she will active the rinnegan is close to non, as this would require larger amounts of Asura and Indra's chakra. Which even took Madara decades while actively producing the chakra through DNA infusion.